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[2602.07135] Landscaper: Understanding Loss Landscapes Through Multi-Dimensional Topological Analysis
Summary
The paper presents Landscaper, an open-source Python package for analyzing loss landscapes in neural networks using multi-dimensional topological analysis, revealing complex geometric structures and improving model diagnostics.
Why It Matters
Understanding loss landscapes is crucial for optimizing neural networks and enhancing generalization. Landscaper offers a novel approach that combines topological data analysis with traditional metrics, providing deeper insights into model performance, particularly in data-scarce scenarios.
Key Takeaways
- Landscaper enables multi-dimensional analysis of loss landscapes.
- Introduces Saddle-Minimum Average Distance (SMAD) to quantify landscape smoothness.
- Demonstrates effectiveness across various architectures and tasks.
- Provides insights into model diagnostics and architecture design.
- Applicable in challenging tasks like chemical property prediction.
Computer Science > Machine Learning arXiv:2602.07135 (cs) [Submitted on 6 Feb 2026 (v1), last revised 21 Feb 2026 (this version, v3)] Title:Landscaper: Understanding Loss Landscapes Through Multi-Dimensional Topological Analysis Authors:Jiaqing Chen, Nicholas Hadler, Tiankai Xie, Rostyslav Hnatyshyn, Caleb Geniesse, Yaoqing Yang, Michael W. Mahoney, Talita Perciano, John F. Hartwig, Ross Maciejewski, Gunther H. Weber View a PDF of the paper titled Landscaper: Understanding Loss Landscapes Through Multi-Dimensional Topological Analysis, by Jiaqing Chen and 10 other authors View PDF HTML (experimental) Abstract:Loss landscapes are a powerful tool for understanding neural network optimization and generalization, yet traditional low-dimensional analyses often miss complex topological features. We present Landscaper, an open-source Python package for arbitrary-dimensional loss landscape analysis. Landscaper combines Hessian-based subspace construction with topological data analysis to reveal geometric structures such as basin hierarchy and connectivity. A key component is the Saddle-Minimum Average Distance (SMAD) for quantifying landscape smoothness. We demonstrate Landscaper's effectiveness across various architectures and tasks, including those involving pre-trained language models, showing that SMAD captures training transitions, such as landscape simplification, that conventional metrics miss. We also illustrate Landscaper's performance in challenging chemical property pre...
